Field-Tuned Order by Disorder in Frustrated Ising Magnets with Antiferromagnetic Interactions

Abstract

We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion, and Monte Carlo simulations to characterize the order-by-disorder transition. By direct evaluation of the density of states, we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in 2D and 3D samples and evaluate how anomalous finite-size effects could be exploited to detect this phenomenon experimentally in two-dimensional artificial systems, or in antiferromagnetic all-in-all-out pyrochlores like Nd 2 Hf 2 O 7 or Nd 2 Zr 2 O 7 , for the first time. DOI: 10.1103/PhysRevLett.117.167203 Order by disorder (OBD) is the mechanism whereby a system with a nontrivially degenerate ground state develops long-range order by the effect of classical or quantum fluctuations [1]. From a theoretical point of view, the OBD mechanism is a relatively common occurrence in geometrically frustrated spin models [2], such as the fully frustrated domino model-where it was discussed for the first time [1]-or the Ising antiferromagnet on the three-dimensional fcc lattice [3]. Many other theoretical realizations exist. However, definitive experimental evidence for this mechanism has remained elusive. Strong evidence for quantum OBD in the antiferromagnetic (AFM) XY insulating rare-earth pyrochlore oxide Er 2 Ti 2 O 7 has been reported [4][5][6][7], but a conclusive proof of thermal OBD remains unseen in the laboratory so far. The difficulty lies in establishing whether order is selected through the OBD mechanism (a huge disproportion in the density of low-energy excitations associated with particular ground states) or is due to energetic contributions not taken into account that actually lift the ground-state degeneracy.In this work we study OBD in Ising spin systems where the staggered order is inhibited by a magnetic field. We analyze theoretically and numerically the threedimensional pyrochlore system and its two-dimensional projection (the checkerboard lattice). We demonstrate the existence of singular finite-size effects (FSE) and we show how they can be exploited to detect OBD. Our results suggest that thermal OBD could be finally observed experimentally in natural staggered structures based on the pyrochlores [8][9][10], as well as in artificially designed two-dimensional magnetic [11] or colloidal systems [12].More precisely, we first study an Ising pyrochlore with h111i anisotropy and AFM nearest-neighbor interactions. In the absence of magnetic field (B), the ground state is the all-spins-in-all-spins-out Néel state [13]. A strong field along the crystalline direction [110] can break this order, turning it into a disordered state with three-spins-in-onespin-out and three-out-one-in elementary units. This type of disordered system of magnetic charges (see below) had been studied before in the context of spi...

Fingerprint of local disorder in long range ordered isometric pyrochlores

“…: Li-ion battery 8,9 , photoluminescence 10,11 , laser materials 12 , solid oxide fuel cells 13,14 …). They possess exotic physical properties 15–18 exuding a strong interest in their modelling and simulation 19,20 . Part of their diversity lies in their high sensitivity to order and disorder which is often associated with the crystalline transition between ordered pyrochlore and the disordered fluorite structures 21–25 .…”

Cluster mean-field study of the Heisenberg model for CuInVO5

“…Interestingly, the temperature dependence of the correlations is nonmonotonic with certain spin-spin correlations strengthening with increasing temperature. Such effects are typically encountered in frustrated magnets where entropic effects at higher temperatures can help in enhancement of order [32][33][34]. We also identify multiple spin-flop transitions in the presence of external field which highlight the inequivalence of spins within a tetramer.…”

On the mechanism behind the inverse melting in systems with competing interactions

“…As can be seen, once we include the nonlinear local dynamics there is an entropy gain due to the soft nature of the order parameter -it is worth noting that local entropy is defined as −S(φ) in Eqs. (2,10). Once these free energy functionals of Eq.…”